Question in description

Question

Suppose an asteroid and a piece of space debris are traveling in the same plane in space. The asteroid follows a path that can be modeled by the equation y=2x^2-3x+1. The space debris follows a path that can be modeled by the equation y=8x-13.

(a) Will the paths of the two objects intersect? Is it possible for the two objects to collide? If so, what are the coordinates of the point where the paths intersect?

(b) What additional information would you need to decide whether the two objects will collide? Explain.

Answer 1

If you graph both functions, you will see that y = 2x²-3x+1 and y = 8x-13 intersect at the point (2,3). This means it is possible for the two objects to collide.

However, we need additional information about when the objects begin this motion / the velocity of the objects in order to know if they will reach the point (2,3) at the same time

Answer 2

Set the two equations equal to each other and rearrange:

2x² - 11x + 14 = 0

Factor: (2x - 4)*(x - 3.5) = 0

This gives:

(2x - 4) = 0, or x = 2, and

(x - 3.5) = 0, or x =3.5.

The lines intersect at x values of 2 and 3.5. The corresponding values of y are 3 and 15. The intercepts are (2, 3) and (3.5, 15).

The quadratic equation produces a parabala and the second is a straight line. Use a graphing calculator to see why it is they intercept in two places.